Writing decimals and fractions shown on number lines

- [Instructor] We're told express the point on the number line as both a fraction and a decimal. So pause this video and have a go at that. All right, now let's do this together. So we can see that the point in question, it's at a higher value than four and it's less than five. So greater than four, less than five. And the space between four and five is divided into one, two, three, four, five, six, seven, eight, nine, 10 equal sections. So each of these hash marks represent an extra tenth. So this is four, then this is four and one tenth, and now this is four right over here and two tenths. So we could write this, if we wanted to write it as a fraction or as a mixed number, this would be four and two tenths. And if we wanted to write that as a decimal, that would be four, and then in the tenths place, well we have two tenths. And that's it, we're done. Let's do another example. So here, we're once again asked to express the point on the number line as both a fraction and a decimal, but this one's a little bit different. Let's see how you can, if you can identify how it is different and answer the question. So pause this video, and once again have a go at it. All right, so here, our point, it's not between two whole numbers. It's actually between two tenths. We're between three and two tenths and three and three tenths. So this is between three and two tenths and three and three tenths. So each of these hash marks, which are a tenth of a tenth. So they would actually be a hundredth. So one way to think about it, you could view 3.2 or three and two tenths as three and 20 hundredths. And you could view three and three tenths as three and 30 hundredths. And so this is three and 20 hundredths. This is three and 21 hundredths, three and 22 hundredths. So this point right over here is three and 22 hundredths, 22 hundredths, and of course, you could also write that as a mixed number. That is three and 22 over 100. Now another way that you could've approached it is hey, I'm starting at 3.2 or three and two tenths, and so I'm starting here at 3.2. And then I'm going to add to that, not just one hundredth, but two hundredths, so it would be three, two tenths, and then two hundredths. And there you have it, we've expressed it as both a fraction and a decimal.